I have some confusion about 3.2-4 in CLRS. Here is the question :
Is the function $\left\lceil \log { n } \right\rceil !$ polynomially bounded? Is the function $\left\lceil \log { \log { n } } \right\rceil !$ polynomially bounded?
There is a point I can't understand.Why $\left\lceil lgn \right\rceil <lgn+1\le 2lgn\quad for\quad all\quad n\ge 2$? I even draw a graph in desmos.
In the graph, I find it should be $n\ge 1.414$ instead of $n\ge 2$. If $n\ge2$, there will never be $\left\lceil lgn \right\rceil =2lgn$.